A New Look At The Path Integral Of Quantum Mechanics

Details A New Look At The Path Integral Of Quantum Mechanics A New Look At The Path Integral Of Quantum Mechanics

2010-09-30

arxiv.org/abs/1009.6032v1

Physics

High Energy Physics

High Energy Physics - Theory

77 pp

Scientific paper

The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct explanation of the relationship of the A-model to quantum mechanics; such a relationship has been explored from several points of view in the last few years. These phenomena have an analog for Chern-Simons gauge theory in three dimensions: integration cycles in the path integral of this theory can be derived from N=4 super Yang-Mills theory in four dimensions. Hence, under certain conditions, a Chern-Simons path integral in three dimensions is equivalent to an N=4 path integral in four dimensions.

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